Question
Find Greatest Common Divisor of 2040 and 629, using Euclidean algorithm.
Answer
The GCD of given numbers is 17.
Explanation
Step 1 :
Divide by and get the remainder
The remainder is positive (), so we will continue with division.
Step 2 :
Divide by and get the remainder
The remainder is still positive (), so we will continue with division.
Step 3 :
Divide by and get the remainder
The remainder is zero => GCD is the last divisor .
We can summarize an algorithm into a following table.
| 2040 | : | 629 | = | 3 | remainder ( 153 ) | ||||
| 629 | : | 153 | = | 4 | remainder ( 17 ) | ||||
| 153 | : | 17 | = | 9 | remainder ( 0 ) | ||||
| GCD = 17 | |||||||||
This solution can be visualized using a Venn diagram.
0,0
2040
629
17
2
2
2
3
5
37
The GCD equals the product of the numbers at the intersection.
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